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A, B and C three friends started the business in which A invested for 4 months, B initially didn’t invest and started as working partner, while C invested for 6 months. They decided to donate 9% of total profit and to give 21% of total profit to B as salary. Find the ratio of their profit shares if A and C invested in the ratio of 3 ∶ 2 and B also invested an amount which is 80% of total amount invested by A and C together for a single month.

A, B and C three friends started the business in which A invested for 4 months, B initially didn’t invest and started as working partner, while C invested for 6 months. They decided to donate 9% of total profit and to give 21% of total profit to B as salary. Find the ratio of their profit shares if A and C invested in the ratio of 3 ∶ 2 and B also invested an amount which is 80% of total amount invested by A and C together for a single month. Correct Answer 30 : 31 : 30

Given:

Ratio of invested money by A and C = 3 ∶ 2

A invested money for 4 months and C invested money for 6 months

Formula:

Profit = invested money × time period

Calculation:

Let A invested 3x and C invested 2x.

Then B invested = (3x + 2x) × 80%

⇒ 5x × 80/100 = 4x

Let total profit be 100%

According to question,

9% is given as donation and B gets 21% as salary of total profits.

Remaining part of profit = 70%

Now ratio of their shares is

3x × 4 ∶ 4x × 1 ∶ 2x ×  6

⇒ 3 ∶ 1 ∶ 3

A gets = 3/7 of 70% = 30%

B gets = 1/7 of 70% + 21% = 31%

C gets = 3/7 of 70% = 30%

∴ Ratio of profit shares of A , B and C = 30 ∶ 31 ∶ 30

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